Physical approach to complex systems

Physics Reports

Volumn 515, Issue 3-4, 2012, Pages 115-226

  Kwapień, Jarosław ^a   Drozdz, Stanisław ^a,b  

^a INSTITUTE OF NUCLEAR PHYSICS   (Poland)

^b CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Asymmetric correlations; Coexistence of collectivity and noise; Complex networks; Complex systems; Complexity measures; Correlations; Critical phenomena; Financial markets; Fractals; Human brain; Multifractals; Quantitative linguistics; Random matrix theory; Time series analysis

Indexed keywords

EID: 84861200374     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2012.01.007     Document Type: Review

References (387)

1. Nagel E. The Structure of Science: Problems in the Logic of Scientific Explanation 1961, Routledge.
2. Kałuszyńska E. Found. Sci. 1998, 1:133-150.
3. Ellis J. Nature 1986, 323:595-598.
4. Gribbin J. The Search for Superstrings, Symmetry, and the Theory of Everything 1999, Little, Brown and Company.
5. Gutzwiller M.C. Rev. Mod. Phys. 1998, 70:589-639.
6. Drozdz S., Nishizaki S., Speth J., Wambach J. Phys. Rep. 1990, 197:1-65.
7. Ellis G.F.R. Nature 2005, 435:743.
8. Weinberg S. Reductionism redux. The New York Review of Books 1995, 42(15):39-42. Reprinted in: S. Weinberg, Facing Up: Science And Its Cultural Adversaries, Harvard Univ. Press, 2001.
9. Dyson F. The scientist as rebel. The New York Review of Books 1995, 42(9):31-33. Reprinted in: F. Dyson, The Scientist as Rebel, Random House Inc., 2006.
10. Laughlin R.B., Pines D. Proc. Nat. Acad. Sci. USA 1999, 97:28-31.
11. Aristotle, Metaphysics, Book VIII (4th century B.C.).
12. Anderson P.W. Science 1972, 177:393-396.
13. Getling A.V. Rayleigh-Bénard Convection: Structures and Dynamics 1997, World Scientific.
14. Frisch U. Turbulence: The Legacy of A.N. Kolmogorov 1996, Cambridge Univ. Press.
15. Stanley H.E. Introduction to Phase Transitions and Critical Phenomena 1987, Oxford Univ. Press.
16. Shpenkov G.P. Friction Surface Phenomena 1995, Elsevier Science.
17. Santamarina J.C., Shin H.S. Friction in granular media. Meso-scale Shear Physics in Earthquake and Landslide Mechanics 2009, 157-188. CRC Press. Y.H. Hatzor, J. Sulem, I. Vardoulakis (Eds.).
18. Mandelbrot B. Science 1967, 156:636-638.
19. Werner B.T. Science 1999, 284:102-104.
20. Wiggs G.F.S. Prog. Phys. Geog. 2001, 25:53-79.
21. Sinden R.R. DNA Structure and Function 1994, Academic Press.
22. Baldwin J.E., Krebs H. Nature 1984, 291:381-382.
23. Winfree A.T. The Geometry of Biological time 2001, Springer. 2nd ed.
24. Klevecz R.R., Bolen J., Forrest G., Murray D.B. Proc. Natl. Acad. Sci. USA 2004, 101:1200-1205.
25. Szathmáry E., Smith J.M. Nature 1995, 374:227-232.
26. Schuster P. Complexity 1996, 2:22-30.
27. Hofbauer J., Sigmund K. Evolutionary Games and Population Dynamics 1998, Cambridge Univ. Press.
28. Michod R.E. Darwinian Dynamics 2000, Princeton Univ. Press.
29. Kelso J.A.S. Dynamic Patterns: The Self-Organization of Brain and Behavior 1995, MIT Press.
30. Chomsky N. Rules and Representations 1980, Columbia Univ. Press.
31. Christiansen M.H., Chatera N. Behav. Brain Sci. 2008, 31:489-509.
32. Yasutomi A. Physica D 1995, 82:180-194.
33. Duffy J., Ochs J. Amer. Econ. Rev. 1999, 89:847-877.
34. Howitt P., Clower R. J. Econ. Behav. Organ. 2000, 41:55-84.
35. Dore M.H.I. The Macrodynamics of Business Cycles: A Comparative Evaluation 1993, WileyBlackwell.
36. Chian A.C.-L. Complex Systems Approach to Economic Dynamics. Lecture Notes in Economics and Mathematical Systems 2007, vol. 592. Springer.
37. Axelrod R. The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration 1997, Princeton Univ. Press.
38. Mesjasz C. Acta Phys. Pol. A 2010, 117:706-715.
39. Mainzer K. Thinking in Complexity 1994, Springer-Verlag.
40. Strogatz S.H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering 2001, Westview Press.
41. Fisher M.E. Rev. Mod. Phys. 1998, 70:653-681.
42. Turcotte D.L. Rep. Prog. Phys. 1999, 62:1377-1429.
43. Haken H. Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics 1977, Springer-Verlag.
44. Ayyub B.M., Klir G.J. Uncertainty Modeling and Analysis in Engineering and the Sciences 2006, Chapman & Hall/CRC.
45. Lloyd S. IEEE Control Syst. Mag. 2001, 21(4):7-8.
46. Kolmogorov A.N. Dokl. Akad. Nauk SSSR 1941, 30:301-305.
47. Gell-Mann M. Complexity 1995, 1:16-19.
48. Gell-Mann M., Lloyd S. Effective complexity. Nonextensive Entropy - Interdisciplinary Applications 2003, 386-398. Oxford Univ. Press. M. Gell-Mann, C. Tsallis (Eds.).
49. Bennett C. Logical depth and physical complexity. The Universal Turing Machine - A Half-Century Survey 1988, 227-257. Oxford Univ. Press. R. Herken (Ed.).
50. N. Ay, M. Müller, A. Szkoła, preprint, 2008. arxiv:0810.5663.
51. Bennett C. Dissipation, information, computational complexity and the definition of organization. Emerging Syntheses in Science 1987, 215-231. Addison-Wesley. D. Pines (Ed.).
52. Wolfram S. Physica D 1984, 10:1-35.
53. Margolus N. Physica D 1984, 10:81-95.
54. Shannon C. Bell Syst. Tech. J. 1948, 27:379-423. 623-656.
55. Lloyd S., Pagels H. Ann. Phys. 1988, 188:186-213.
56. Schrödinger E. What is life? 1944, Cambridge Univ. Press.
57. Bar-Yam Y. Complexity 2004, 7:47-63.
58. Metzler R., Bar-Yam Y. Phys. Rev. E 2005, 71:046114.
59. Fraser A.M., Swinney H.L. Phys. Rev. A 1986, 33:1134-1140.
60. Bennett C. How to define complexity in physics, and why. SFI Studies in the Sciences of Complexity 1990, vol. VIII:148. Addison-Wesley.
61. Prigogine I. From Being to Becoming. Time and Complexity in the Physical Sciences 1980, W.H. Freeman & Co.
62. Prigogine I. Etude thermodynamics des phenomenes irreversibles 1945, l'Université Libre de Bruxelles.
63. Turing A.M. Phil. Trans. R. Soc. Lond. B 1952, 237:37-72.
64. Barabási A.-L., Stanley H.E. Fractal Concepts in Surface Growth 1995, Cambridge Univ. Press.
65. Gutenberg B., Richter R.F. Bull. Seism. Soc. Am. 1944, 34:185-188.
66. West G.B., Brown J.H., Enquist B.J. Science 1997, 276:122-126.
67. Brown J.H., Gillooly J.F., Allen A.P., Savage V.M., West G.B. Ecology 2004, 85:1771-1789.
68. Souma W. Physics of personal income. Empirical Science of Financial Fluctuations 2002, 343-352. Springer-Verlag. H. Takayasu (Ed.).
69. Malamud B.D., Turcotte D.L., Guzzetti F., Reichenbach P. Earth Surf. Process. Landforms 2004, 29:687-711.
70. Barabási A.-L., Albert R. Science 1999, 286:509-512.
71. Sornette D. Critical Phenomena In Natural Sciences 2006, Springer-Verlag.
72. Witten T.A.Jr., Sander L.M. Phys. Rev. Lett. 1981, 47:1400-1403.
73. Yule G.U. Phil. Trans. R. Soc. Lon. B 1925, 213:21-87.
74. Newman M.E.J. Contemp. Phys. 2005, 46:323-351.
75. Stanley H.E. Rev. Mod. Phys. 1999, 71:S358-S366.
76. Bak P., Tang C., Weisenfeld K. Phys. Rev. E 1988, 38:364-374.
77. Johnson J.B. Phys. Rev. 1925, 26:71-85.
78. Hooge F.N. Phys. Lett. A 1969, 29:139-140.
79. Voss R.F., Clarke J. Phys. Rev. Lett. 1976, 36:42-44.
80. Mandelbrot B.B., Wallis J.R. Water Resour. Res. 1968, 5:909-918.
81. Taft B.A. Deep Sea Res. 1974, 21:403-430.
82. Press W.H. Comments Astrophys. 1978, 7:103-119.
83. Gilden D.L., Thornton T., Mallon M.W. Science 1995, 267:1837-1839.
84. Chen Y., Ding M., Kelso J.A.S. Phys. Rev. Lett. 1997, 79:4501-4504.
85. Billock V.A., Guzman G.C.de., Kelso J.A.S. Physica D 2001, 148:136-146.
86. Kobayashi M., Musha T. IEEE Trans. Biol. Eng. 1982, 29:456-457.
87. Pilgram B., Kaplan D.T. Am. J. Physiol. 1999, 276:R1-R9.
88. Kulessa B., Srokowski T., Drozdz S. Acta Phys. Pol. B 2003, 34:3-15.
89. Voss R.F., Clarke J. Nature 1975, 258:317-318.
90. Dutta P., Horn P.M. Rev. Mod. Phys. 1981, 53:497-516.
91. Weissman M.B. Rev. Mod. Phys. 1988, 60:537-571.
92. Kadanoff L.P., Nagel S.R., Wu L., Zhou S.-M. Phys. Rev. A 1989, 39:6524-6537.
93. Jaeger H.M., Liu C.-H., Nagel S.R. Phys. Rev. Lett. 1989, 62:40-43.
94. Held G.A., Solina D.H., Keane D.T., Haag W.J., Horn P.M., Grinstein G. Phys. Rev. Lett. 1993, 65:1120-1123.
95. Bak P., Sneppen K. Phys. Rev. Lett. 1993, 71:4083-4086.
96. Gould S.J., Eldredge N. Paleobiology 1977, 3:115-151.
97. Huang Y., Saleur H., Sammis C.G., Sornette D. Europhys. Lett. 1999, 41:43-48.
98. Sornette D. Proc. Natl. Acad. Sci. USA 2002, 99:2522-2529.
99. Carlson J.M., Doyle J. Phys. Rev. E 1999, 60:1412-1427.
100. Carlson J.M., Doyle J. Proc. Natl. Acad. Sci. USA 2002, 99:2538-2545.
101. Lisman J. Trends Neurosci. 1997, 20:38-43.
102. Abeles M., Prut Y., Bergman H., Vaadia E. Progress in Brain Research 1994, 102:395-404.
103. Güémez J., Matías M.A. Physica D 1996, 96:334-343.
104. Érdi P. Complexity Explained 2007, Springer-Verlag.
105. Tononi G., Edelman G., Sporns O. Trends Cogn. Sci. 1998, 2:474-484.
106. Friston K.J. Neuroimage 1997, 5:164-171.
107. Kauffman S.A. The Origins of Order: Self-organization and Selection in Evolution 1993, Oxford Univ. Press.
108. Freeman W., Kozma R., Werbos P. BioSystems 2001, 59:109-123.
109. Tsuda I., Barna G. How can chaos be a cognitive processor?. Towards the Harnessing of Chaos 1994, 47-61. Elsevier Science. M. Yamaguti (Ed.).
110. Chialvo D.R. Nature Physics 2010, 6:744-750.
111. Stassinopoulos D., Bak P. Phys. Rev. E 1995, 51:5033-5039.
112. Chialvo D.R. Physica A 2004, 340:756-765.
113. Eguíluz V.M., Chialvo D.R., Cecchi G.A., Baliki M., Apkarian A.V. Phys. Rev. Lett. 2005, 94:018102.
114. Kubota K. Ann. Nucl. Med. 2001, 15:471-486.
115. Matthews P.M., Honey G.D., Bullmore E.T. Nat. Rev. Neurosci. 2006, 7:732-744.
116. deCharms R.C. Nature Reviews Neuroscience 2008, 9:720-729.
117. Hämäläinen M., Hari R., Ilmoniemi R.J., Knuutila J., Lounasmaa O.V. Rev. Mod. Phys. 1993, 65:413-497.
118. Del Gratta C., Pizzella V., Tecchio F., Romani G.L. Rep. Prog. Phys. 2001, 64:1759-1814.
119. Ioannides A.A. The Neuroscientist 2006, 12:524-544.
120. Beckner C., Blythe R., Bybee J., Christiansen M.H., Croft W., Ellis N.C., Holland J., Ke J., Larsen-Freeman D., Schoenemann T. Language Learning 2009, 59(Supl. 1).
121. Pinker S., Bloom P. Behav. Brain Sci. 1990, 13:707-727.
122. van Everbroeck E. Linguistic Typology 2003, 7:1-50.
123. Nowak M.A., Krakauer D.C. Proc. Natl. Acad. Sci. USA 1999, 96:8028-8033.
124. Nowak M.A., Plotkin J.B., Jansen V.A.A. Nature 2000, 404:495-498.
125. Arthur W.B. Science 1999, 284:107-109.
126. Farmer J.D. Ind. Corp. Change 2002, 11:895-953.
127. Burda Z., Jurkiewicz J., Nowak M.A. Acta Phys. Pol. B 2003, 34:87-131.
128. Farmer J.D., Geanakoplos J. Complexity 2009, 14:11-38.
129. Fama E. J. Business 1965, 38:34-105.
130. Sornette D. Phys. Rep. 2003, 378:1-98.
131. Bouchaud J.-P., Farmer J.D., Lillo F. How markets slowely digest changes in demand and supply. Handbook of Financial Markets: Dynamics and Evolution 2008, Elsevier: Academic Press. T. Hens, K. Schenk-Hoppe (Eds.).
132. Bartolozzi M., Leinweber D.B., Thomas A.W. Physica A 2005, 350:451-465.
133. Bouchaud J.-P., Cont R. Eur. Phys. J. B 1998, 6:543-550.
134. Gopikrishnan P., Plerou V., Gabaix X., Stanley H.E. Phys. Rev. E 2000, 62:R4493-R4496.
135. Plerou V., Gopikrishnan P., Amaral L.A.N., Gabaix X., Stanley H.E. Phys. Rev. E 2000, 62:R3023-R3026.
136. Lillo F., Farmer J.D. Stud. Nonlinear Dyn. Econom. 2004, 8:1-33.
137. Lillo F., Farmer J.D. Fluct. Noise Lett. 2005, 5:L209-L216.
138. Tóth B., Kertész J., Farmer J.D. Eur. Phys. J. B 2009, 71:499-510.
139. Baillie R.T., Chung C.-F., Tieslau M.A. J. Appl. Econom. 1995, 11:23-40.
140. Diebold F.X., Rudebusch G.D. J. Monetary Econ. 1989, 24:189-209.
141. Stanley M.H.R., Amaral L.A.N., Buldyrev S.V., Havlin S., Leschhorn H., Maass P., Salinger M.A., Stanley H.E. Nature 1996, 379:804-806.
142. Liu Y., Gopikrishnan P., Cizeau P., Meyer M., Peng C.-K., Stanley H.E. Phys. Rev. E 1999, 60:1390-1400.
143. Matia K., Amaral L.A.N., Goodwin S.P., Stanley H.E. Phys.Rev. E 2002, 66:045103(R).
144. Plerou V., Gopikrishnan P., Amaral L.A.N., Meyer M., Stanley H.E. Phys. Rev. E 1999, 60:6519-6529.
145. Gopikrishnan P., Plerou V., Amaral L.A.N., Meyer M., Stanley H.E. Phys. Rev. E 1999, 60:5305-5316.
146. Müller U.A., Dacorogna M.M., Olsen R.B., Pictet O.V., Schwarz M., Morgenegg C. J. Banking Finance 1990, 14:1189-1208.
147. Bank For International Settlements "Triennial Central Bank Survey", 2010, http://www.bis.org.
148. International Monetary Fund, http://www.imf.org.
149. World Federation of Exchanges, http://www.world-exchanges.org.
150. Schaden M. Physica A 2002, 316:511-538.
151. Maslov S. Physica A 2001, 301:397-406.
152. Drozdz S., Grümmer F., Ruf F., Speth J. Physica A 2001, 294:226-234.
153. Drozdz S., Kwapień J., Speth J., Wójcik M. Physica A 2002, 314:355-361.
154. Brody T.A., Flores J., French J.B., Mello P.A., Pendey A., Wong S.S.M. Rev. Mod. Phys. 1981, 53:385-479.
155. Guhr T., Müller-Groeling A., Weidenmüller H.A. Phys. Rep. 1998, 299:189-425.
156. Wishart J. Biometrica 1928, 20:32.
157. Marčenko V.A., Pastur L.A. Math. USSR Sb. 1967, 1:457-483.
158. Sengupta A.M., Mitra P.P. Phys. Rev. E 1999, 60:003389.
159. Tracy C.A., Widom H. The distribution of the largest eigenvalue in the Gaussian ensembles. CRM Series in Mathematical Physics 2000, vol. 4:461-472. Springer-Verlag. J.F. van Diejen, L. Vinet (Eds.).
160. Johnstone I. Ann. Stat. 2001, 29:296-327.
161. Bassler K.E., Forrester P.J., Frankel N.E. J. Math. Phys. 2009, 50:033302.
162. Baik J., Ben arous G., Péché S. Ann. Prob. 2005, 33:1643-1697.
163. Trades and Quotes Database, http://www.nyxdata.com.
164. Karlsruher Kapitalmarktdatenbank Karlsruhe University, http://fmi.fbv.uni-karlsruhe.de.
165. Laloux L., Cizeau P., Bouchaud J.-P., Potters M. Phys. Rev. Lett. 1999, 83:1467-1470.
166. Plerou V., Gopikrishnan P., Rosenow B., Amaral L.A.N., Stanley H.E. Phys. Rev. Lett. 1999, 83:1471-1474.
167. Plerou V., Gopikrishnan P., Rosenow B., Amaral L.A.N., Gühr T., Stanley H.E. Phys. Rev. E 2002, 65:066126.
168. Utsugi A., Ino K., Oshikawa M. Phys.Rev. E 2004, 70:026110.
169. Kwapień J., Drozdz S., Oświȩcimka P. Acta Phys. Pol. B 2005, 36:2423-2434.
170. Malevergne Y., Sornette D. Physica A 2004, 331:660-668.
171. Noh J.D. Phys. Rev. E 2000, 61:5981-5982.
172. Tumminello C., Lillo F., Mantegna R.N. Europhys. Lett. 2007, 78:30006.
173. Markowitz H. J. Finance 1952, 7:77-91.
174. Kwapień J., Drozdz S., Oświȩcimka P. Physica A 2006, 359:589-606.
175. Burda Z., Jurkiewicz J. Physica A 2004, 344:67-72.
176. Burda Z., Görlich A., Jurkiewicz J., Wacław B. Eur. Phys. J. B 2006, 49:319-323.
177. Bonanno G., Lillo F., Mantegna R.N. Quant. Finance 2001, 1:96-104.
178. Kwapień J., Drozdz S., Speth J. Physica A 2004, 337:231-242.
179. Conlon T., Ruskin H.J., Crane M. Adv. Compl. Sys. 2009, 12:439-454.
180. Epps T.W. J. Am. Stat. Assoc. 1979, 74:291-298.
181. Tóth B., Kertész J. Quant. Finance 2009, 9:793-802.
182. Tóth B., Kertész J. Physica A 2005, 360:505-515.
183. Drozdz S., Górski A.Z., Kwapień J. Eur. Phys. J. B 2007, 58:499-502.
184. Kwapień J., Gworek S., Drozdz S., Górski A.Z. J. Econ. Interact. Coord. 2009, 4:55-72.
185. Kim D.-H., Jeong H. Phys. Rev. E 2005, 72:046133.
186. M. Kaciczak, Correlations on the world financial markets, Master Thesis, Supervisor: J. Kwapień, Univ. of Science and Technology, Kraków 2006, (in Polish).
187. Mizuno T., Takayasu H., Takayasu M. Physica A 2006, 364:336-342.
188. Naylor M.J., Rose L.C., Moyle B.J. Physica A 2007, 382:199-208.
189. Górski A.Z., Drozdz S., Kwapień J. Eur. Phys. J. B 2008, 66:91-96.
190. Kwapień J., Drozdz S., Ioannides A.A. Phys. Rev. E 2000, 62:5557-5564.
191. Drozdz S., Kwapień J., Grümmer F., Ruf F., Speth J. Physica A 2001, 299:144-153.
192. Kwapień J., Drozdz S., Grümmer F., Ruf F., Septh J. Physica A 2002, 309:171-182.
193. Liu L.C., Ioannides A.A., Streit M. Brain Topogr. 1999, 11:291-303.
194. Ioannides A.A., Liu L.C., Kwapień J., Drozdz S., Streit M. Hum. Brain Mapp. 2000, 11:77-92.
195. Ioannides A.A., Liu M.J., Liu L.C., Bamidis P.D., Hellstrand E., Stephan K.M. Int. J. Psychophysiol. 1995, 20:161-175.
196. Odom J.V., Bach M., Barber C., Brigell M., Marmor M.F., Tormene A.P., Holder G.E., Vaegan Doc. Ophthalmol. 2004, 108:115-123.
197. Liu L.C., Ioannides A.A., Müller-Gärtner H.W. Neuroimage 1998, 8:149-162.
198. Drozdz S., Kwapień J., Ioannides A.A. Acta Phys. Pol. B 2011, 42:987-999.
199. Biely C., Thurner S. Quant. Finance 2008, 8:705-722.
200. Kanzieper E., Singh N. J. Math. Phys. 2010, 51:103510.
201. Ginibre J. J. Math. Phys. 1965, 6:440-449.
202. Edelman A., Kostlan E., Shub M. J. Amer. Math. Soc. 1994, 7:247-267.
203. Edelman A. J. Multivariate Anal. 1997, 60:203-232.
204. Sommers H.-J., Wieczorek W. J. Phys. A: Math. Theor. 2008, 41:405003.
205. Sommers H.-J., Crisanti A., Sompolinsky H., Stein Y. Phys. Rev. Lett. 1988, 60:1895-1898.
206. Forrester P.J., Nagao T. Phys. Rev. Lett. 2007, 99:050603.
207. Morris J.S., Frith C.D., Perrett D.I., Rowland D., Young A.W., Calder A.J., Dolan R.J. Nature 1996, 383:812-815.
208. Walter W.G., Cooper R., Aldridge V.J., Mccallum C., Cohen J. Electroenceph. Clin. Neurophysiol. 1964, 17:340-344.
209. Pantev C.C., Lütkenhöner B., Hoke M.M., Lehnertz K. Audiology 1986, 25:54-61.
210. Nakasato N., Fujita S., Seki K., Kawamura T., Matani A., Tamura I., Fujiwara S., Yoshimoto T. Electroen. Clin. Neurophysiol. 1995, 94:183-190.
211. Kwapień J., Drozdz S., Liu L.C., Ioannides A.A. Phys. Rev. E 1998, 58:6359-6367.
212. Kwapień J., Drozdz S., Górski A.Z., Oświȩcimka P. Acta Phys. Pol. B 2006, 37:3039-3048.
213. Stephanov M. Phys. Rev. Lett. 1996, 76:4472-4475.
214. Janik R.A., Nowak M.A., Papp G., Zahed I. Nucl. Phys. B 1997, 501:603-642.
215. Akemann G., Wettig T. Phys. Rev. Lett. 2004, 92:102002.
216. Drozdz S., Trellakis A., Wambach J. Phys. Rev. Lett. 1996, 76:4891-4894.
217. Fyodorov Y., Koruzhenko B., Sommers H.-J. Phys. Rev. Lett. 1997, 79:557-560.
218. Drozdz S., Okołowicz J., Płoszajczak M., Rotter I. Phys. Rev. C 2000, 62:024313.
219. Timme M., Wolf F., Geisel T. Phys. Rev. Lett. 2004, 92:074101.
220. Bouchaud J.-P., Potters M. Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management 2000, Cambridge Univ. Press.
221. Paul W., Baschnagel J. Stochastic Processes. From Physics to Finance 1999, Springer-Verlag.
222. Mantegna R.N., Stanley H.E. Phys. Rev. Lett. 1994, 73:2946-2949.
223. Koponen I. Phys. Rev. E 1995, 52:1197-1199.
224. Laherrère J., Sornette D. Eur. Phys. J. B 1998, 2:525-539.
225. Bachelier L. Ann. Sci. l'École Norm. Sup. 1900, 3:21-86.
226. Black F., Scholes M. J. Polit. Econ. 1973, 81:637-654.
227. Mandelbrot B. J. Business 1963, 36:394-419.
228. Mantegna R.N., Stanley H.E. Nature 1995, 376:46-49.
229. Lux T. Appl. Financ. Econom. 1996, 6:463-475.
230. Rak R., Drozdz S., Kwapień J. Physica A 2007, 374:315-324.
231. Pan R.K., Sinha S. Europhys. Lett. 2007, 77:58004.
232. Schmitt F., Schertzer D., Lovejoy S. Appl. Stoch. Mod. D. A. 1999, 15:29-53.
233. Skjeltorp J.A. Physica A 2000, 283:486-528.
234. Couto miranda L., Riera R. Physica A 2001, 297:509-520.
235. Oh G., Um C.-J., Kim S. J. Korean Phys. Soc. 2006, 48:S197-S201.
236. Lux T., Marchesi M. Nature 1998, 397:498-500.
237. Gabaix X., Gopikrishnan P., Plerou V., Stanley H.E. Nature 2003, 423:267-270.
238. Farmer J.D., Gillemot L., Lillo F., Mike S., Sen A. Quant. Finance 2004, 4:383-397.
239. S. Thurner, J.D. Farmer, J. Geanakoplos, Leverage causes fat tails and clustered volatility, preprint, 2009. arxiv:0908.1555.
240. Ding Z., Granger C.W.J., Engle R. J. Empir. Finance 1993, 1:83-106.
241. Bouchaud J.-P. Physica A 2000, 285:18-28.
242. Ghashghaie S., Breymann W., Peinke J., Talkner P., Dodge Y. Nature 1996, 381:767-770.
243. A. Arneodo, J.-P. Bouchaud, R. Cont, J.-F. Muzy, M. Potters, D. Sornette, Comment on "Turbulent cascades in foreign exchange markets", preprint, 1996. arxiv:cond-mat/9607120.
244. Arneodo A., Muzy J.-F., Sornette D. Eur. Phys. J. B 1998, 2:277-282.
245. Bouchaud J.-P., Gefen Y., Potters M., Wyart M. Quant. Finance 2004, 4:176-190.
246. Kwapień J., Drozdz S., Speth J. Physica A 2003, 330:605-621.
247. Drozdz S., Grümmer F., Górski A.Z., Ruf F., Speth J. Physica A 2000, 287:440-449.
248. Sandoval L., De Paula Franca I. Correlations of financial markets in times of crisis. Physica A 2012, 391:187-208.
249. Drozdz S., Kwapień J., Grümmer F., Speth J. Acta Phys. Pol. B 2003, 34:4293-4306.
250. Drozdz S., Forczek M., Kwapień J., Oświȩcimka P., Rak R. Physica A 2007, 383:59-64.
251. Tsallis C. Introduction to Nonextensive Statistical Mechanics 2009, Springer.
252. Tsallis C. J. Stat. Phys. 1988, 52:479-487.
253. Tsallis C., Levy S.V.F., Souza A.M.C., Maynard R. Phys. Rev. Lett. 1995, 75:3589-3593.
254. Moyano L.G., Tsallis C., Gell-Mann M. Europhys. Lett. 2006, 73:813-819.
255. Queiros S.M.D., Tsallis C. AIP Conf. Proc. 2007, 965:21-33.
256. Tsallis C., Anteneodo C., Borland L., Osorio R. Physica A 2003, 324:89-100.
257. Drozdz S., Kwapień J., Oświȩcimka P., Rak R. New. J. Phys. 2010, 12:105003.
258. Estoup J.-B. Gammes sténographiques. Methodes et exercises pour l'acquisition de la vitesse 1916, Institut Sténographique de France.
259. Thorndike E.L. A Teacher's Word Book of 20,000 Words 1932, Teacher's College.
260. Zipf G.K. Selective Studies and the Principle of Relative Frequency in Language 1932, MIT Press.
261. Zipf G.K. Human Behavior and the Principle of Least Effort 1949, Addison-Wesley.
262. Axtell R.L. Science 2001, 293:1818-1820.
263. Redner S. Eur. Phys. J. B 1998, 4:131-134.
264. Mandelbrot B. Trans. I.R.E. 1954, 3:124-137.
265. Cohen A., Mantegna R.N., Havlin S. Fractals 1997, 5:95-104.
266. Ferrer i Cancho R., Solé R.V. Proc. Natl. Acad. Sci. USA 2003, 100:788-791.
267. Ferrer i Cancho R. Eur. Phys. J. B 2005, 44:249-257.
268. Simon H.A. Biometrika 1955, 42:425-440.
269. Miller G.A. Amer. J. Psychol. 1957, 70:311-314.
270. Li W. IEEE Trans. Inf. Theory 1992, 38:1842-1845.
271. Ferrer i Cancho R., Solé R.V. Adv. Complex Syst. 2002, 5:1-6.
272. Ferrer i Cancho R., Riordan O., Bollobás B. Proc. R. Soc. Lond. B 2005, 272:561-565.
273. Montemurro M.A. Physica A 2001, 300:567-578.
274. Ferrer i Cancho R., Solé R.V. J. Quant. Ling. 2001, 8:165-173.
275. Kwapień J., Drozdz S., Orczyk A. Acta Phys. Pol. A 2010, 117:716-720.
276. J. Joyce, Ulisses, transl. by M. Słomczyński, Wydawnictwo Pomorze, 1992.
277. Miyazima S., Lee Y., Nagamine T., Miyajima H. Physica A 2000, 278:272-288.
278. Zanette D.H., Manrubia S.C. Physica A 2001, 295:1-16.
279. Yamada H.S., Iguchi K. Physica A 2008, 387:1628-1636.
280. L.Q. Ha, P. Hanna, J. Ming, F.J. Smith, Artif. Intell. Rev., doi:10.1007/s10462-009-9135-4.
281. Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., Shraiman B.I. Phys. Rev. A 1986, 33:1141-1151.
282. Barabási A.-L., Vicsek T. Phys. Rev. A 1991, 44:2730-2733.
283. Hentschel H.G.E., Procaccia I. Physica D 1983, 8:435-444.
284. Peng C.-K., Buldyrev S.V., Havlin S., Simons M., Stanley H.E., Goldberger A.L. Phys. Rev. E 1994, 49:1685-1689.
285. Kantelhardt J.W., Zschiegner S.A., Koscielny-Bunde E., Bunde A., Havlin S., Stanley H.E. Physica A 2002, 316:87-114.
286. Muzy J.F., Bacry E., Arneodo A. Internat. J. Bifur Chaos Appl. Sci. Engrg. 1994, 2:245-302.
287. Arneodo A., Bacry E., Muzy J.F. Physica A 1995, 213:232-275.
288. Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Series in Appl. Math. 1992, SIAM.
289. Oświȩcimka P., Kwapień J., Drozdz S. Phys. Rev. E 2006, 74:016103.
290. Jaffard S. Probab. Theory Related Fields 1999, 114:207-227.
291. Nakao H. Phys. Lett. A 2000, 266:282-289.
292. Amitrano C., Coniglio A., Meakin P., Zanetti M. Phys. Rev. B 1987, 44:4974-4977.
293. Stanley H.E., Meakin P. Nature 1988, 335:405-409.
294. Jensen M.H., Kadanoff L.P., Libchaber A., Procaccia I., Stavans J. Phys. Rev. Lett. 1985, 55:2798-2801.
295. Muzy J.-F., Bacry E., Arneodo A. Phys. Rev. Lett. 1991, 67:3515-3518.
296. Labini F.S., Montouri M., Pietronero L. J. Physique IV 1998, 8. Pr-115-Pr-118.
297. Ashkenazy Y., Baker D.R., Gildor H., Havlin S. Geophys. Res. Lett. 2003, 30:2146-2149.
298. Ivanov P.C., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Struzik Z.R., Stanley H.E. Nature 1999, 399:461-465.
299. A. Fisher, L. Calvet, B. Mandelbrot, Multifractality of Deutschemark/US dollar exchange rates, Cowles Foundation Discussion Paper 1166, 1997.
300. Ivanova K., Ausloos M. Physica A 1999, 265:279-291.
301. Matteo T.Di., Aste T., Dacorogna M.M. Physica A 2003, 324:183-188.
302. Bershadskii A. Physica A 2003, 317:591-596.
303. Matia K., Ashkenazy Y., Stanley H.E. Europhys. Lett. 2003, 61:422-428.
304. Oświȩcimka P., Kwapień J., Drozdz S. Physica A 2005, 347:626-638.
305. Eisler Z., Kertész J. Eur. Phys. J. B 2006, 51:145-154.
306. Jiang Z.-Q., Chen W., Zhou W.-X. Physica A 2009, 388:433-440.
307. Ren F., Zhou W.-X. Europhys. Lett. 2008, 84:68001.
308. Eisler Z., Kertész J. Europhys. Lett. 2007, 77:28001.
309. L. Borland, J.-P. Bouchaud, J.-F. Muzy, G. Zumbach, The dynamics of financial markets - Mandelbrot's multifractal cascades and beyond, Wilmott Magazine, preprint, 2005, arxiv:cond-mat/0501292.
310. L. Calvet, A. Fisher, B. Mandelbrot, Large deviations and the distributions of price changes, Cowles Foundation Discussion Paper 1165, 1997.
311. T. Lux, Detecting multi-fractal properties in asset returns: the failure of the 'scaling estimator', University of Kiel, Working Paper, 2003.
312. Eisler Z., Kertész J. Physica A 2004, 343:603-622.
313. Bacry E., Delour J., Muzy J.-F. Phys. Rev. E 2001, 64:026103.
314. Czarnecki Ł, Grech D. Acta Phys. Pol. A 2010, 117:623-629.
315. Eisler Z., Kertész J., Yook S.H., Barabási A.-L. Europhys. Lett. 2005, 69:664-670.
316. Rak R., Drozdz S., Kwapień J., Oświȩcimka P. Acta Phys. Pol. B 2005, 36:2459-2468.
317. Kwapień J., Oświȩcimka P., Drozdz S. Physica A 2005, 350:466-474.
318. Lim G., Kim S., Lee H., Kim K., Lee D.I. Physica A 2007, 386:259-266.
319. Kumar S., Deo N. Physica A 2009, 388:1593-1602.
320. Su Z.Y., Wang Y.T., Huang H.Y. J. Korean Phys. Soc. 2009, 54:1395-1402.
321. Zhou W.-X. Europhys. Lett. 2010, 88:28004.
322. Drozdz S., Kwapień J., Oświȩcimka P., Rak R. Europhys. Lett. 2009, 88:60003.
323. Bouchaud J.-P., Potters M., Meyer M. Eur. Phys. J. B 2000, 13:595-599.
324. Bianchi S. Appl. Econ. Lett. 2007, 12:775-780.
325. Sornette D. Phys. Rep. 1998, 297:240-270.
326. Nauenberg J. J. Phys. A 1975, 8:925-928.
327. Jona-Lasinio G. Nuovo Cimento B 1975, 26:99-119.
328. Feigenbaum J.A., Freund P.G.O. Internat. J. Modern Phys. B 1996, 10:3737-3745.
329. Sornette D., Johansen A., Bouchaud J.-P. J. Physique I 1996, 6:167-175.
330. Drozdz S., Ruf F., Speth J., Wójcik M. Eur. Phys. J. B 1999, 10:589-593.
331. Oświȩcimka P., Drozdz S., Kwapień J., Górski A.Z. Acta Phys. Pol. A 2010, 117:637-639.
332. Kozłowska M., Kutner R. Acta Phys. Pol. A 2010, 118:677-687.
333. Harras G., Sornette D. J. Econ. Behav. Org. 2011, 80:137-152.
334. Sornette D., Johansen A. Physica A 1998, 261:581-598.
335. Johansen A., Sornette D. Eur. Phys. J. B 1999, 9:167-174.
336. Johansen A., Ledoit O., Sornette D. Int. J. Theor. Appl. Finance 2000, 3:219-255.
337. Johansen A., Sornette D. Physica A 2001, 294:465-502.
338. Drozdz S., Grümmer F., Ruf F., Speth J. Physica A 2003, 324:174-182.
339. Johansen A., Sornette D. Eur. Phys. J. B 2000, 17:319-328.
340. Drozdz S., Kwapień J., Oświȩcimka P., Speth J. Acta Phys. Pol. A 2008, 114:539-546.
341. Drozdz S., Kwapień J., Oświȩcimka P. Acta Phys. Pol. A 2008, 114:699-702.
342. Laloux L., Potters M., Cont R., Aguilar J.-P., Bouchaud J.-P. Europhys. Lett. 1999, 45:1-5.
343. D. Brée, N.L. Joseph, Fitting the log periodic power law to financial crashes: a critical analysis, 2010, preprint no. arxiv:1002.1010.
344. D. Brée, D. Challet, P.P. Peirano, Prediction accuracy and sloppiness of log-periodic functions, 2010, preprint no. arxiv:1006.2010.
345. Yan W., Woodard R., Sornette D. Phys. Procedia 2010, 3:1641-1657.
346. Bartolozzi M., Drozdz S., Leinweber D.B., Speth J., Thomas A.W. Internat. J. Modern Phys. C 2005, 16:1347-1361.
347. (conducted by S. Drozdz, J. Kwapień, and P. Oświȩcimka). http://picasaweb.google.com/finpredict.
348. Barabási A.-L. Science 2009, 325:412-413.
349. Onnela J.-P., Saramaki J., Kertész J., Kaski K. Phys. Rev. E 2005, 71:065103(R).
350. Albert R., Jeong H., Barabási A.-L. Nature 1999, 401:130-131.
351. Percacci R., Vespignani A. Eur. Phys. J. B 2003, 32:411-414.
352. Barrat A., Barthélemy M., Pastor-Satorras R., Vespignani A. Proc. Natl. Acad. Sci. USA 2004, 101:3747-3752.
353. Guimerà R., Mossa S., Turtschi A., Amaral L.A.N. Proc. Nat. Acad. Sci. USA 2005, 102:7794-7799.
354. Bachnik W., Szymczyk S., Leszczyński P., Podsiadło R., Rymszewicz E., Kuryło Ł, Makowiec D., Bykowska B. Acta Phys. Pol. B 2005, 36:3179-3191.
355. Krawczyk M., Muchnik L., Mańka-Krasoń A., Kułakowski K. Physica A 2011, 390:2611-2618.
356. Liljeros F., Edling C.R., Amaral L.A.N., Stanley H.E., Aberg Y. Nature 2001, 411:907-908.
357. Pastor-Satorras R., Vespignani A. Phys. Rev. Lett. 2001, 86:3200-3203.
358. Ma H., Zeng A.-P. Bioinformatics 2003, 19:270-277.
359. Tanaka R. Phys. Rev. Lett. 2005, 94:168101.
360. Stuart J.M., Segal E., Koller D., Kim S.K. Science 2003, 302:249-255.
361. Boccaletti S., Latora V., Moreno Y., Chavez M., Hwang D.-U. Phys. Rep. 2006, 424:175-308.
362. Barthélemy M. Phys. Rep. 2011, 499:1-101.
363. Ferrer i Cancho R., Solé R.V. Proc. R. Soc. Lond. B 2001, 268:2261-2265.
364. Ferrer i Cancho R., Solé R.V., Koehler R. Phys. Rev. E 2004, 69:051915.
365. Fukś H. Proc. 2009 IEEE Toronto Int. Conf. - Science and Technology for Humanity 2009, IEEE, pp. 491-496.
366. Albert R., Jeong H., Barabási A.-L. Nature 2000, 406:378-382.
367. Travers J., Milgram S. Sociometry 1969, 32:425-443.
368. Watts D.J., Strogatz S.H. Nature 1998, 393:440-442.
369. Fronczak A., Fronczak P., Hołyst J.A. Phys. Rev. E 2004, 70:056110.
370. Mantegna R.N. Eur. Phys. J. B 1999, 11:193-197.
371. Bonanno G., Caldarelli G., Lillo F., Miccichè S., Vandewalle N., Mantegna R.N. Eur. Phys. J. B 2004, 38:363-371.
372. Sieczka P., Hołyst J.A. Physica A 2009, 388:1621-1630.
373. Drozdz S., Kwapień J., Speth J. AIP Conf. Proc. 2010, 1261:256-264.
374. Coronnello C., Tumminello M., Lillo F., Miccichè S., Mantegna R.N. Acta Phys. Pol. B 2005, 36:2653-2679.
375. Bonanno G., Caldarelli G., Lillo F., Mantegna R.N. Phys. Rev. E 2003, 68:046130.
376. Fortunato S. Phys. Rep. 2010, 486:75-174.
377. Ortega G.J., Matesanz D. Internat. J. Modern Phys. C 2006, 17:333-341.
378. Kwapień J., Gworek S., Drozdz S., Górski A.Z. Acta Phys. Pol. B 2009, 40:175-194.
379. Song D.-M., Tumminello M., Zhou W.-X., Mantegna R.N. Phys. Rev. E 2011, 84:026108.
380. Miccichè S., Bonanno G., Lillo F., Mantegna R.N. Physica A 2003, 324:66-73.
381. McDonald M., Suleman O., Williams S., Howison S., Johnson N.F. Phys. Rev. E 2005, 72:046106.
382. D.J. Fenn, M.A. Porter, P.J. Mucha, M. Mcdonald, S. Williams, N.F. Johnson, N.S. Jones, Dynamical clustering of exchange rates, 2009, preprint arxiv:0905.4912.
383. Wolfram S. A New Kind of Science 2002, Wolfram Media.
384. Stigler S.M. Trans. N. Y. Acad. Sci. 1980, 39:147-158.
385. S. Drozdz, The science of complexity: with the Bible along Wall Street, Nasza Politechnika no. 91, Cracow Univ. of Technology, 2011, pp. 23-26 (in Polish).
386. Mandelbrot B.B. Fractals and Scaling in Finance 1997, Springer.
387. Merton R.K. Science 1968, 159:56-63.